If you are a member of ANY organization for choral directors (ACDA, MENC, etc.), you can see that this happens all the time. Choirs from all over are assembled into huge mega-choirs that tour, etc. Of course, this is not cheap - and a significant source of revenue for the organizers, travel agencies, etc, that do all the work to make this happen, beyond the music. You sound like an amateur singer with a big heart - but realize that these things are a LOT bigger and harder to organize that some grass-roots campaign.
Added - I went back to check you other questions, and found that 7 months ago, you asked about starting a professional marching band; I have quite a bit of professional band experience. At that time, I got the BA to your question, and my answer here is essentially the same - your heart may be in the right place, but the BUSINESS of making things work our in the arts is what is daunting. I have owned a chamber music business in NY since 1984 (I am primarily a flutist, altho it was my keyboard and conducting skills that were my main source of employment for years), and it is the management of the WORK, not the management of the music and musicians, that take most of the effort - and why we take a larger slice of the paycheck than anyone who plays FOR us.
Professional choral director from 1971 to 2008. Professional classical musician, and certified, multi-degreed teacher and competition judge in NY. Music business owner since 1984.